X+2x/3x=40

Solution for X+2x/3x=40 equation:

X+2X/3X=40

We move all terms to the left:

X+2X/3X-(40)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X+2X-40*3X=0

We add all the numbers together, and all the variables

2X+X*3X-40*3X=0

Wy multiply elements

3X^2+2X-120X=0

We add all the numbers together, and all the variables

3X^2-118X=0

a = 3; b = -118; c = 0;
Δ = b2-4ac
Δ = -1182-4·3·0
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-118}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+118}{2*3}=\frac{236}{6}
=39+1/3
$